LMFDB - Embedded newform 6027.2.a.bb.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1258372982$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	8.8.7457527933.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 6x^{6} + 23x^{5} - 4x^{4} - 27x^{3} + 8x^{2} + 8x + 1 $ x^8 - 3x^7 - 6x^6 + 23x^5 - 4x^4 - 27x^3 + 8x^2 + 8*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.35554$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.04183 q^{2} -1.00000 q^{3} +2.16908 q^{4} -3.68950 q^{5} +2.04183 q^{6} -0.345232 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.04183 q^{2} -1.00000 q^{3} +2.16908 q^{4} -3.68950 q^{5} +2.04183 q^{6} -0.345232 q^{8} +1.00000 q^{9} +7.53333 q^{10} +0.232219 q^{11} -2.16908 q^{12} +2.59232 q^{13} +3.68950 q^{15} -3.63325 q^{16} +4.71395 q^{17} -2.04183 q^{18} -7.74581 q^{19} -8.00281 q^{20} -0.474151 q^{22} +8.48752 q^{23} +0.345232 q^{24} +8.61238 q^{25} -5.29308 q^{26} -1.00000 q^{27} -4.10946 q^{29} -7.53333 q^{30} -10.4125 q^{31} +8.10896 q^{32} -0.232219 q^{33} -9.62509 q^{34} +2.16908 q^{36} -8.13831 q^{37} +15.8156 q^{38} -2.59232 q^{39} +1.27373 q^{40} -1.00000 q^{41} +2.59910 q^{43} +0.503701 q^{44} -3.68950 q^{45} -17.3301 q^{46} +3.41324 q^{47} +3.63325 q^{48} -17.5850 q^{50} -4.71395 q^{51} +5.62294 q^{52} -3.35153 q^{53} +2.04183 q^{54} -0.856770 q^{55} +7.74581 q^{57} +8.39082 q^{58} -8.02496 q^{59} +8.00281 q^{60} +13.1267 q^{61} +21.2607 q^{62} -9.29063 q^{64} -9.56434 q^{65} +0.474151 q^{66} +6.60562 q^{67} +10.2249 q^{68} -8.48752 q^{69} +3.23226 q^{71} -0.345232 q^{72} -6.63277 q^{73} +16.6171 q^{74} -8.61238 q^{75} -16.8013 q^{76} +5.29308 q^{78} -5.24998 q^{79} +13.4049 q^{80} +1.00000 q^{81} +2.04183 q^{82} +2.50998 q^{83} -17.3921 q^{85} -5.30693 q^{86} +4.10946 q^{87} -0.0801693 q^{88} +13.2734 q^{89} +7.53333 q^{90} +18.4101 q^{92} +10.4125 q^{93} -6.96926 q^{94} +28.5781 q^{95} -8.10896 q^{96} -7.90714 q^{97} +0.232219 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 8 q^{3} + 13 q^{4} - 7 q^{5} - q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + q^2 - 8 * q^3 + 13 * q^4 - 7 * q^5 - q^6 + 6 * q^8 + 8 * q^9	$ 8 q + q^{2} - 8 q^{3} + 13 q^{4} - 7 q^{5} - q^{6} + 6 q^{8} + 8 q^{9} - 8 q^{10} + 11 q^{11} - 13 q^{12} - 10 q^{13} + 7 q^{15} - 17 q^{16} - 3 q^{17} + q^{18} - 6 q^{19} - 11 q^{20} + 15 q^{22} + 14 q^{23} - 6 q^{24} + 25 q^{25} - 24 q^{26} - 8 q^{27} + 2 q^{29} + 8 q^{30} - 16 q^{31} + 3 q^{32} - 11 q^{33} + 4 q^{34} + 13 q^{36} - 20 q^{37} - 10 q^{38} + 10 q^{39} + 3 q^{40} - 8 q^{41} + 7 q^{43} - 7 q^{45} - 5 q^{46} - 14 q^{47} + 17 q^{48} - 5 q^{50} + 3 q^{51} - 23 q^{52} + 7 q^{53} - q^{54} - 48 q^{55} + 6 q^{57} - 20 q^{58} - 22 q^{59} + 11 q^{60} + 33 q^{62} - 10 q^{64} - 14 q^{65} - 15 q^{66} + 12 q^{67} + 27 q^{68} - 14 q^{69} - 5 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} - 25 q^{75} - 43 q^{76} + 24 q^{78} - 15 q^{79} + 7 q^{80} + 8 q^{81} - q^{82} - 15 q^{83} - 43 q^{85} + 31 q^{86} - 2 q^{87} + 17 q^{88} - 29 q^{89} - 8 q^{90} + 19 q^{92} + 16 q^{93} - 20 q^{94} + 14 q^{95} - 3 q^{96} - 19 q^{97} + 11 q^{99}+O(q^{100}) $ 8 * q + q^2 - 8 * q^3 + 13 * q^4 - 7 * q^5 - q^6 + 6 * q^8 + 8 * q^9 - 8 * q^10 + 11 * q^11 - 13 * q^12 - 10 * q^13 + 7 * q^15 - 17 * q^16 - 3 * q^17 + q^18 - 6 * q^19 - 11 * q^20 + 15 * q^22 + 14 * q^23 - 6 * q^24 + 25 * q^25 - 24 * q^26 - 8 * q^27 + 2 * q^29 + 8 * q^30 - 16 * q^31 + 3 * q^32 - 11 * q^33 + 4 * q^34 + 13 * q^36 - 20 * q^37 - 10 * q^38 + 10 * q^39 + 3 * q^40 - 8 * q^41 + 7 * q^43 - 7 * q^45 - 5 * q^46 - 14 * q^47 + 17 * q^48 - 5 * q^50 + 3 * q^51 - 23 * q^52 + 7 * q^53 - q^54 - 48 * q^55 + 6 * q^57 - 20 * q^58 - 22 * q^59 + 11 * q^60 + 33 * q^62 - 10 * q^64 - 14 * q^65 - 15 * q^66 + 12 * q^67 + 27 * q^68 - 14 * q^69 - 5 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 - 25 * q^75 - 43 * q^76 + 24 * q^78 - 15 * q^79 + 7 * q^80 + 8 * q^81 - q^82 - 15 * q^83 - 43 * q^85 + 31 * q^86 - 2 * q^87 + 17 * q^88 - 29 * q^89 - 8 * q^90 + 19 * q^92 + 16 * q^93 - 20 * q^94 + 14 * q^95 - 3 * q^96 - 19 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.04183	−1.44379	−0.721897	−	0.692001i	$-0.756729\pi$
$2$	−2.04183	−1.44379	−0.721897	+	0.692001i	$0.756729\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.16908	1.08454
$5$	−3.68950	−1.64999	−0.824996	−	0.565138i	$-0.808823\pi$
$5$	−3.68950	−1.64999	−0.824996	+	0.565138i	$0.808823\pi$
$6$	2.04183	0.833575
$7$	0	0
$7$	0	0
$8$	−0.345232	−0.122058
$9$	1.00000	0.333333
$10$	7.53333	2.38225
$11$	0.232219	0.0700165	0.0350083	−	0.999387i	$-0.488854\pi$
$11$	0.232219	0.0700165	0.0350083	+	0.999387i	$0.488854\pi$
$12$	−2.16908	−0.626159
$13$	2.59232	0.718979	0.359490	−	0.933149i	$-0.382951\pi$
$13$	2.59232	0.718979	0.359490	+	0.933149i	$0.382951\pi$
$14$	0	0
$15$	3.68950	0.952624
$16$	−3.63325	−0.908313
$17$	4.71395	1.14330	0.571650	−	0.820497i	$-0.306303\pi$
$17$	4.71395	1.14330	0.571650	+	0.820497i	$0.306303\pi$
$18$	−2.04183	−0.481265
$19$	−7.74581	−1.77701	−0.888505	−	0.458866i	$-0.848256\pi$
$19$	−7.74581	−1.77701	−0.888505	+	0.458866i	$0.848256\pi$
$20$	−8.00281	−1.78948
$21$	0	0
$22$	−0.474151	−0.101089
$23$	8.48752	1.76977	0.884885	−	0.465810i	$-0.154237\pi$
$23$	8.48752	1.76977	0.884885	+	0.465810i	$0.154237\pi$
$24$	0.345232	0.0704702
$25$	8.61238	1.72248
$26$	−5.29308	−1.03806
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−4.10946	−0.763107	−0.381554	−	0.924347i	$-0.624611\pi$
$29$	−4.10946	−0.763107	−0.381554	+	0.924347i	$0.624611\pi$
$30$	−7.53333	−1.37539
$31$	−10.4125	−1.87015	−0.935074	−	0.354454i	$-0.884667\pi$
$31$	−10.4125	−1.87015	−0.935074	+	0.354454i	$0.884667\pi$
$32$	8.10896	1.43347
$33$	−0.232219	−0.0404241
$34$	−9.62509	−1.65069
$35$	0	0
$36$	2.16908	0.361513
$37$	−8.13831	−1.33793	−0.668965	−	0.743294i	$-0.733262\pi$
$37$	−8.13831	−1.33793	−0.668965	+	0.743294i	$0.733262\pi$
$38$	15.8156	2.56564
$39$	−2.59232	−0.415103
$40$	1.27373	0.201395
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	2.59910	0.396360	0.198180	−	0.980166i	$-0.436497\pi$
$43$	2.59910	0.396360	0.198180	+	0.980166i	$0.436497\pi$
$44$	0.503701	0.0759357
$45$	−3.68950	−0.549998
$46$	−17.3301	−2.55518
$47$	3.41324	0.497872	0.248936	−	0.968520i	$-0.419919\pi$
$47$	3.41324	0.497872	0.248936	+	0.968520i	$0.419919\pi$
$48$	3.63325	0.524415
$49$	0	0
$50$	−17.5850	−2.48690
$51$	−4.71395	−0.660085
$52$	5.62294	0.779761
$53$	−3.35153	−0.460368	−0.230184	−	0.973147i	$-0.573933\pi$
$53$	−3.35153	−0.460368	−0.230184	+	0.973147i	$0.573933\pi$
$54$	2.04183	0.277858
$55$	−0.856770	−0.115527
$56$	0	0
$57$	7.74581	1.02596
$58$	8.39082	1.10177
$59$	−8.02496	−1.04476	−0.522380	−	0.852713i	$-0.674956\pi$
$59$	−8.02496	−1.04476	−0.522380	+	0.852713i	$0.674956\pi$
$60$	8.00281	1.03316
$61$	13.1267	1.68070	0.840351	−	0.542042i	$-0.182349\pi$
$61$	13.1267	1.68070	0.840351	+	0.542042i	$0.182349\pi$
$62$	21.2607	2.70011
$63$	0	0
$64$	−9.29063	−1.16133
$65$	−9.56434	−1.18631
$66$	0.474151	0.0583640
$67$	6.60562	0.807005	0.403503	−	0.914978i	$-0.367793\pi$
$67$	6.60562	0.807005	0.403503	+	0.914978i	$0.367793\pi$
$68$	10.2249	1.23996
$69$	−8.48752	−1.02178
$70$	0	0
$71$	3.23226	0.383599	0.191800	−	0.981434i	$-0.438568\pi$
$71$	3.23226	0.383599	0.191800	+	0.981434i	$0.438568\pi$
$72$	−0.345232	−0.0406860
$73$	−6.63277	−0.776307	−0.388153	−	0.921595i	$-0.626887\pi$
$73$	−6.63277	−0.776307	−0.388153	+	0.921595i	$0.626887\pi$
$74$	16.6171	1.93169
$75$	−8.61238	−0.994472
$76$	−16.8013	−1.92724
$77$	0	0
$78$	5.29308	0.599323
$79$	−5.24998	−0.590669	−0.295334	−	0.955394i	$-0.595431\pi$
$79$	−5.24998	−0.590669	−0.295334	+	0.955394i	$0.595431\pi$
$80$	13.4049	1.49871
$81$	1.00000	0.111111
$82$	2.04183	0.225483
$83$	2.50998	0.275506	0.137753	−	0.990467i	$-0.456012\pi$
$83$	2.50998	0.275506	0.137753	+	0.990467i	$0.456012\pi$
$84$	0	0
$85$	−17.3921	−1.88644
$86$	−5.30693	−0.572261
$87$	4.10946	0.440580
$88$	−0.0801693	−0.00854607
$89$	13.2734	1.40698	0.703490	−	0.710705i	$-0.251624\pi$
$89$	13.2734	1.40698	0.703490	+	0.710705i	$0.251624\pi$
$90$	7.53333	0.794083
$91$	0	0
$92$	18.4101	1.91939
$93$	10.4125	1.07973
$94$	−6.96926	−0.718825
$95$	28.5781	2.93206
$96$	−8.10896	−0.827617
$97$	−7.90714	−0.802848	−0.401424	−	0.915892i	$-0.631485\pi$
$97$	−7.90714	−0.802848	−0.401424	+	0.915892i	$0.631485\pi$
$98$	0	0
$99$	0.232219	0.0233388
$100$	18.6809	1.86809
$101$	−10.8529	−1.07990	−0.539950	−	0.841697i	$-0.681557\pi$
$101$	−10.8529	−1.07990	−0.539950	+	0.841697i	$0.681557\pi$
$102$	9.62509	0.953026
$103$	−5.28687	−0.520931	−0.260465	−	0.965483i	$-0.583876\pi$
$103$	−5.28687	−0.520931	−0.260465	+	0.965483i	$0.583876\pi$
$104$	−0.894950	−0.0877571
$105$	0	0
$106$	6.84326	0.664676
$107$	6.23899	0.603146	0.301573	−	0.953443i	$-0.402488\pi$
$107$	6.23899	0.603146	0.301573	+	0.953443i	$0.402488\pi$
$108$	−2.16908	−0.208720
$109$	4.43703	0.424990	0.212495	−	0.977162i	$-0.431841\pi$
$109$	4.43703	0.424990	0.212495	+	0.977162i	$0.431841\pi$
$110$	1.74938	0.166797
$111$	8.13831	0.772454
$112$	0	0
$113$	19.5852	1.84243	0.921213	−	0.389060i	$-0.127200\pi$
$113$	19.5852	1.84243	0.921213	+	0.389060i	$0.127200\pi$
$114$	−15.8156	−1.48127
$115$	−31.3147	−2.92011
$116$	−8.91374	−0.827620
$117$	2.59232	0.239660
$118$	16.3856	1.50842
$119$	0	0
$120$	−1.27373	−0.116275
$121$	−10.9461	−0.995098
$122$	−26.8025	−2.42659
$123$	1.00000	0.0901670
$124$	−22.5856	−2.02825
$125$	−13.3279	−1.19208
$126$	0	0
$127$	15.3392	1.36114	0.680568	−	0.732685i	$-0.261733\pi$
$127$	15.3392	1.36114	0.680568	+	0.732685i	$0.261733\pi$
$128$	2.75199	0.243244
$129$	−2.59910	−0.228838
$130$	19.5288	1.71279
$131$	17.1723	1.50035	0.750176	−	0.661239i	$-0.229969\pi$
$131$	17.1723	1.50035	0.750176	+	0.661239i	$0.229969\pi$
$132$	−0.503701	−0.0438415
$133$	0	0
$134$	−13.4876	−1.16515
$135$	3.68950	0.317541
$136$	−1.62741	−0.139549
$137$	9.02525	0.771079	0.385540	−	0.922691i	$-0.374015\pi$
$137$	9.02525	0.771079	0.385540	+	0.922691i	$0.374015\pi$
$138$	17.3301	1.47524
$139$	11.0833	0.940071	0.470036	−	0.882647i	$-0.344241\pi$
$139$	11.0833	0.940071	0.470036	+	0.882647i	$0.344241\pi$
$140$	0	0
$141$	−3.41324	−0.287447
$142$	−6.59974	−0.553838
$143$	0.601984	0.0503404
$144$	−3.63325	−0.302771
$145$	15.1618	1.25912
$146$	13.5430	1.12083
$147$	0	0
$148$	−17.6526	−1.45104
$149$	10.2152	0.836862	0.418431	−	0.908249i	$-0.362580\pi$
$149$	10.2152	0.836862	0.418431	+	0.908249i	$0.362580\pi$
$150$	17.5850	1.43581
$151$	−5.71699	−0.465242	−0.232621	−	0.972567i	$-0.574730\pi$
$151$	−5.71699	−0.465242	−0.232621	+	0.972567i	$0.574730\pi$
$152$	2.67410	0.216898
$153$	4.71395	0.381100
$154$	0	0
$155$	38.4170	3.08573
$156$	−5.62294	−0.450195
$157$	−5.45503	−0.435359	−0.217679	−	0.976020i	$-0.569849\pi$
$157$	−5.45503	−0.435359	−0.217679	+	0.976020i	$0.569849\pi$
$158$	10.7196	0.852804
$159$	3.35153	0.265794
$160$	−29.9180	−2.36522
$161$	0	0
$162$	−2.04183	−0.160422
$163$	12.6634	0.991874	0.495937	−	0.868358i	$-0.334825\pi$
$163$	12.6634	0.991874	0.495937	+	0.868358i	$0.334825\pi$
$164$	−2.16908	−0.169377
$165$	0.856770	0.0666994
$166$	−5.12496	−0.397774
$167$	−11.4402	−0.885268	−0.442634	−	0.896702i	$-0.645956\pi$
$167$	−11.4402	−0.885268	−0.442634	+	0.896702i	$0.645956\pi$
$168$	0	0
$169$	−6.27990	−0.483069
$170$	35.5118	2.72363
$171$	−7.74581	−0.592337
$172$	5.63766	0.429868
$173$	−12.2561	−0.931818	−0.465909	−	0.884833i	$-0.654273\pi$
$173$	−12.2561	−0.931818	−0.465909	+	0.884833i	$0.654273\pi$
$174$	−8.39082	−0.636107
$175$	0	0
$176$	−0.843709	−0.0635970
$177$	8.02496	0.603193
$178$	−27.1021	−2.03139
$179$	−6.29779	−0.470719	−0.235359	−	0.971908i	$-0.575627\pi$
$179$	−6.29779	−0.470719	−0.235359	+	0.971908i	$0.575627\pi$
$180$	−8.00281	−0.596494
$181$	18.8748	1.40296	0.701478	−	0.712691i	$-0.252524\pi$
$181$	18.8748	1.40296	0.701478	+	0.712691i	$0.252524\pi$
$182$	0	0
$183$	−13.1267	−0.970354
$184$	−2.93016	−0.216014
$185$	30.0263	2.20757
$186$	−21.2607	−1.55891
$187$	1.09467	0.0800500
$188$	7.40359	0.539962
$189$	0	0
$190$	−58.3518	−4.23328
$191$	7.98832	0.578014	0.289007	−	0.957327i	$-0.406675\pi$
$191$	7.98832	0.578014	0.289007	+	0.957327i	$0.406675\pi$
$192$	9.29063	0.670493
$193$	−8.36539	−0.602154	−0.301077	−	0.953600i	$-0.597346\pi$
$193$	−8.36539	−0.602154	−0.301077	+	0.953600i	$0.597346\pi$
$194$	16.1451	1.15915
$195$	9.56434	0.684917
$196$	0	0
$197$	−20.1945	−1.43880	−0.719401	−	0.694595i	$-0.755583\pi$
$197$	−20.1945	−1.43880	−0.719401	+	0.694595i	$0.755583\pi$
$198$	−0.474151	−0.0336965
$199$	2.42833	0.172140	0.0860700	−	0.996289i	$-0.472569\pi$
$199$	2.42833	0.172140	0.0860700	+	0.996289i	$0.472569\pi$
$200$	−2.97327	−0.210242
$201$	−6.60562	−0.465925
$202$	22.1597	1.55915
$203$	0	0
$204$	−10.2249	−0.715888
$205$	3.68950	0.257686
$206$	10.7949	0.752116
$207$	8.48752	0.589923
$208$	−9.41854	−0.653058
$209$	−1.79872	−0.124420
$210$	0	0
$211$	−10.1756	−0.700514	−0.350257	−	0.936654i	$-0.613906\pi$
$211$	−10.1756	−0.700514	−0.350257	+	0.936654i	$0.613906\pi$
$212$	−7.26973	−0.499287
$213$	−3.23226	−0.221471
$214$	−12.7390	−0.870819
$215$	−9.58938	−0.653991
$216$	0.345232	0.0234901
$217$	0	0
$218$	−9.05967	−0.613598
$219$	6.63277	0.448201
$220$	−1.85840	−0.125293
$221$	12.2200	0.822009
$222$	−16.6171	−1.11526
$223$	18.3685	1.23004	0.615022	−	0.788510i	$-0.289147\pi$
$223$	18.3685	1.23004	0.615022	+	0.788510i	$0.289147\pi$
$224$	0	0
$225$	8.61238	0.574159
$226$	−39.9898	−2.66008
$227$	16.6244	1.10340	0.551700	−	0.834042i	$-0.313979\pi$
$227$	16.6244	1.10340	0.551700	+	0.834042i	$0.313979\pi$
$228$	16.8013	1.11269
$229$	−15.2296	−1.00640	−0.503200	−	0.864170i	$-0.667844\pi$
$229$	−15.2296	−1.00640	−0.503200	+	0.864170i	$0.667844\pi$
$230$	63.9393	4.21603
$231$	0	0
$232$	1.41872	0.0931433
$233$	14.7310	0.965057	0.482528	−	0.875880i	$-0.339719\pi$
$233$	14.7310	0.965057	0.482528	+	0.875880i	$0.339719\pi$
$234$	−5.29308	−0.346019
$235$	−12.5931	−0.821486
$236$	−17.4068	−1.13308
$237$	5.24998	0.341023
$238$	0	0
$239$	12.3660	0.799889	0.399945	−	0.916539i	$-0.369029\pi$
$239$	12.3660	0.799889	0.399945	+	0.916539i	$0.369029\pi$
$240$	−13.4049	−0.865281
$241$	10.7234	0.690754	0.345377	−	0.938464i	$-0.387751\pi$
$241$	10.7234	0.690754	0.345377	+	0.938464i	$0.387751\pi$
$242$	22.3500	1.43672
$243$	−1.00000	−0.0641500
$244$	28.4729	1.82279
$245$	0	0
$246$	−2.04183	−0.130182
$247$	−20.0796	−1.27763
$248$	3.59474	0.228266
$249$	−2.50998	−0.159064
$250$	27.2133	1.72112
$251$	−10.5518	−0.666026	−0.333013	−	0.942922i	$-0.608065\pi$
$251$	−10.5518	−0.666026	−0.333013	+	0.942922i	$0.608065\pi$
$252$	0	0
$253$	1.97096	0.123913
$254$	−31.3201	−1.96520
$255$	17.3921	1.08914
$256$	12.9622	0.810135
$257$	−26.8542	−1.67512	−0.837561	−	0.546344i	$-0.816019\pi$
$257$	−26.8542	−1.67512	−0.837561	+	0.546344i	$0.816019\pi$
$258$	5.30693	0.330395
$259$	0	0
$260$	−20.7458	−1.28660
$261$	−4.10946	−0.254369
$262$	−35.0630	−2.16620
$263$	22.8337	1.40799	0.703993	−	0.710207i	$-0.251399\pi$
$263$	22.8337	1.40799	0.703993	+	0.710207i	$0.251399\pi$
$264$	0.0801693	0.00493408
$265$	12.3655	0.759604
$266$	0	0
$267$	−13.2734	−0.812320
$268$	14.3281	0.875229
$269$	−26.4506	−1.61272	−0.806360	−	0.591424i	$-0.798566\pi$
$269$	−26.4506	−1.61272	−0.806360	+	0.591424i	$0.798566\pi$
$270$	−7.53333	−0.458464
$271$	8.75300	0.531707	0.265854	−	0.964013i	$-0.414346\pi$
$271$	8.75300	0.531707	0.265854	+	0.964013i	$0.414346\pi$
$272$	−17.1270	−1.03848
$273$	0	0
$274$	−18.4280	−1.11328
$275$	1.99996	0.120602
$276$	−18.4101	−1.10816
$277$	6.44745	0.387390	0.193695	−	0.981062i	$-0.437953\pi$
$277$	6.44745	0.387390	0.193695	+	0.981062i	$0.437953\pi$
$278$	−22.6302	−1.35727
$279$	−10.4125	−0.623382
$280$	0	0
$281$	−21.5896	−1.28793	−0.643965	−	0.765055i	$-0.722712\pi$
$281$	−21.5896	−1.28793	−0.643965	+	0.765055i	$0.722712\pi$
$282$	6.96926	0.415014
$283$	0.145666	0.00865894	0.00432947	−	0.999991i	$-0.498622\pi$
$283$	0.145666	0.00865894	0.00432947	+	0.999991i	$0.498622\pi$
$284$	7.01104	0.416029
$285$	−28.5781	−1.69282
$286$	−1.22915	−0.0726812
$287$	0	0
$288$	8.10896	0.477825
$289$	5.22132	0.307137
$290$	−30.9579	−1.81791
$291$	7.90714	0.463525
$292$	−14.3870	−0.841935
$293$	−7.84054	−0.458049	−0.229025	−	0.973421i	$-0.573554\pi$
$293$	−7.84054	−0.458049	−0.229025	+	0.973421i	$0.573554\pi$
$294$	0	0
$295$	29.6081	1.72385
$296$	2.80960	0.163305
$297$	−0.232219	−0.0134747
$298$	−20.8577	−1.20826
$299$	22.0023	1.27243
$300$	−18.6809	−1.07854
$301$	0	0
$302$	11.6731	0.671713
$303$	10.8529	0.623481
$304$	28.1425	1.61408
$305$	−48.4309	−2.77315
$306$	−9.62509	−0.550230
$307$	−20.8939	−1.19248	−0.596238	−	0.802808i	$-0.703338\pi$
$307$	−20.8939	−1.19248	−0.596238	+	0.802808i	$0.703338\pi$
$308$	0	0
$309$	5.28687	0.300759
$310$	−78.4411	−4.45516
$311$	−28.5586	−1.61941	−0.809706	−	0.586836i	$-0.800373\pi$
$311$	−28.5586	−1.61941	−0.809706	+	0.586836i	$0.800373\pi$
$312$	0.894950	0.0506666
$313$	29.9521	1.69299	0.846497	−	0.532394i	$-0.178707\pi$
$313$	29.9521	1.69299	0.846497	+	0.532394i	$0.178707\pi$
$314$	11.1382	0.628568
$315$	0	0
$316$	−11.3876	−0.640604
$317$	−13.5173	−0.759204	−0.379602	−	0.925150i	$-0.623939\pi$
$317$	−13.5173	−0.759204	−0.379602	+	0.925150i	$0.623939\pi$
$318$	−6.84326	−0.383751
$319$	−0.954292	−0.0534301
$320$	34.2777	1.91618
$321$	−6.23899	−0.348227
$322$	0	0
$323$	−36.5134	−2.03166
$324$	2.16908	0.120504
$325$	22.3260	1.23842
$326$	−25.8565	−1.43206
$327$	−4.43703	−0.245368
$328$	0.345232	0.0190622
$329$	0	0
$330$	−1.74938	−0.0963002
$331$	−0.476790	−0.0262068	−0.0131034	−	0.999914i	$-0.504171\pi$
$331$	−0.476790	−0.0262068	−0.0131034	+	0.999914i	$0.504171\pi$
$332$	5.44435	0.298797
$333$	−8.13831	−0.445976
$334$	23.3589	1.27814
$335$	−24.3714	−1.33155
$336$	0	0
$337$	−20.8216	−1.13422	−0.567111	−	0.823641i	$-0.691939\pi$
$337$	−20.8216	−1.13422	−0.567111	+	0.823641i	$0.691939\pi$
$338$	12.8225	0.697452
$339$	−19.5852	−1.06372
$340$	−37.7248	−2.04592
$341$	−2.41799	−0.130941
$342$	15.8156	0.855212
$343$	0	0
$344$	−0.897294	−0.0483788
$345$	31.3147	1.68592
$346$	25.0250	1.34535
$347$	9.11769	0.489463	0.244732	−	0.969591i	$-0.421300\pi$
$347$	9.11769	0.489463	0.244732	+	0.969591i	$0.421300\pi$
$348$	8.91374	0.477827
$349$	−10.4817	−0.561071	−0.280535	−	0.959844i	$-0.590512\pi$
$349$	−10.4817	−0.561071	−0.280535	+	0.959844i	$0.590512\pi$
$350$	0	0
$351$	−2.59232	−0.138368
$352$	1.88305	0.100367
$353$	4.33421	0.230687	0.115343	−	0.993326i	$-0.463203\pi$
$353$	4.33421	0.230687	0.115343	+	0.993326i	$0.463203\pi$
$354$	−16.3856	−0.870886
$355$	−11.9254	−0.632936
$356$	28.7911	1.52593
$357$	0	0
$358$	12.8590	0.679620
$359$	1.63625	0.0863578	0.0431789	−	0.999067i	$-0.486251\pi$
$359$	1.63625	0.0863578	0.0431789	+	0.999067i	$0.486251\pi$
$360$	1.27373	0.0671316
$361$	40.9976	2.15777
$362$	−38.5393	−2.02558
$363$	10.9461	0.574520
$364$	0	0
$365$	24.4716	1.28090
$366$	26.8025	1.40099
$367$	19.6883	1.02772	0.513861	−	0.857873i	$-0.328215\pi$
$367$	19.6883	1.02772	0.513861	+	0.857873i	$0.328215\pi$
$368$	−30.8373	−1.60751
$369$	−1.00000	−0.0520579
$370$	−61.3086	−3.18728
$371$	0	0
$372$	22.5856	1.17101
$373$	−1.93972	−0.100435	−0.0502175	−	0.998738i	$-0.515991\pi$
$373$	−1.93972	−0.100435	−0.0502175	+	0.998738i	$0.515991\pi$
$374$	−2.23513	−0.115576
$375$	13.3279	0.688248
$376$	−1.17836	−0.0607693
$377$	−10.6530	−0.548658
$378$	0	0
$379$	−3.47525	−0.178512	−0.0892559	−	0.996009i	$-0.528449\pi$
$379$	−3.47525	−0.178512	−0.0892559	+	0.996009i	$0.528449\pi$
$380$	61.9883	3.17993
$381$	−15.3392	−0.785852
$382$	−16.3108	−0.834533
$383$	−10.0079	−0.511382	−0.255691	−	0.966759i	$-0.582303\pi$
$383$	−10.0079	−0.511382	−0.255691	+	0.966759i	$0.582303\pi$
$384$	−2.75199	−0.140437
$385$	0	0
$386$	17.0807	0.869386
$387$	2.59910	0.132120
$388$	−17.1512	−0.870721
$389$	21.7567	1.10311	0.551553	−	0.834140i	$-0.314035\pi$
$389$	21.7567	1.10311	0.551553	+	0.834140i	$0.314035\pi$
$390$	−19.5288	−0.988878
$391$	40.0097	2.02338
$392$	0	0
$393$	−17.1723	−0.866228
$394$	41.2339	2.07733
$395$	19.3698	0.974599
$396$	0.503701	0.0253119
$397$	23.6233	1.18562	0.592811	−	0.805342i	$-0.298018\pi$
$397$	23.6233	1.18562	0.592811	+	0.805342i	$0.298018\pi$
$398$	−4.95825	−0.248535
$399$	0	0
$400$	−31.2910	−1.56455
$401$	−3.67183	−0.183362	−0.0916812	−	0.995788i	$-0.529224\pi$
$401$	−3.67183	−0.183362	−0.0916812	+	0.995788i	$0.529224\pi$
$402$	13.4876	0.672699
$403$	−26.9926	−1.34460
$404$	−23.5407	−1.17119
$405$	−3.68950	−0.183333
$406$	0	0
$407$	−1.88987	−0.0936772
$408$	1.62741	0.0805686
$409$	18.6205	0.920724	0.460362	−	0.887731i	$-0.347720\pi$
$409$	18.6205	0.920724	0.460362	+	0.887731i	$0.347720\pi$
$410$	−7.53333	−0.372045
$411$	−9.02525	−0.445183
$412$	−11.4676	−0.564970
$413$	0	0
$414$	−17.3301	−0.851727
$415$	−9.26056	−0.454583
$416$	21.0210	1.03064
$417$	−11.0833	−0.542750
$418$	3.67269	0.179637
$419$	−20.3870	−0.995971	−0.497985	−	0.867185i	$-0.665927\pi$
$419$	−20.3870	−0.995971	−0.497985	+	0.867185i	$0.665927\pi$
$420$	0	0
$421$	−24.4425	−1.19125	−0.595627	−	0.803261i	$-0.703096\pi$
$421$	−24.4425	−1.19125	−0.595627	+	0.803261i	$0.703096\pi$
$422$	20.7768	1.01140
$423$	3.41324	0.165957
$424$	1.15706	0.0561916
$425$	40.5983	1.96931
$426$	6.59974	0.319759
$427$	0	0
$428$	13.5329	0.654136
$429$	−0.601984	−0.0290641
$430$	19.5799	0.944227
$431$	7.83717	0.377503	0.188752	−	0.982025i	$-0.439556\pi$
$431$	7.83717	0.377503	0.188752	+	0.982025i	$0.439556\pi$
$432$	3.63325	0.174805
$433$	10.6522	0.511914	0.255957	−	0.966688i	$-0.417610\pi$
$433$	10.6522	0.511914	0.255957	+	0.966688i	$0.417610\pi$
$434$	0	0
$435$	−15.1618	−0.726954
$436$	9.62427	0.460919
$437$	−65.7427	−3.14490
$438$	−13.5430	−0.647110
$439$	−24.6501	−1.17649	−0.588243	−	0.808684i	$-0.700180\pi$
$439$	−24.6501	−1.17649	−0.588243	+	0.808684i	$0.700180\pi$
$440$	0.295784	0.0141010
$441$	0	0
$442$	−24.9513	−1.18681
$443$	−0.888234	−0.0422013	−0.0211006	−	0.999777i	$-0.506717\pi$
$443$	−0.888234	−0.0422013	−0.0211006	+	0.999777i	$0.506717\pi$
$444$	17.6526	0.837757
$445$	−48.9722	−2.32151
$446$	−37.5054	−1.77593
$447$	−10.2152	−0.483162
$448$	0	0
$449$	−19.6747	−0.928505	−0.464252	−	0.885703i	$-0.653677\pi$
$449$	−19.6747	−0.928505	−0.464252	+	0.885703i	$0.653677\pi$
$450$	−17.5850	−0.828967
$451$	−0.232219	−0.0109347
$452$	42.4820	1.99818
$453$	5.71699	0.268608
$454$	−33.9443	−1.59308
$455$	0	0
$456$	−2.67410	−0.125226
$457$	−8.76520	−0.410019	−0.205009	−	0.978760i	$-0.565722\pi$
$457$	−8.76520	−0.410019	−0.205009	+	0.978760i	$0.565722\pi$
$458$	31.0963	1.45303
$459$	−4.71395	−0.220028
$460$	−67.9240	−3.16697
$461$	5.76370	0.268442	0.134221	−	0.990951i	$-0.457147\pi$
$461$	5.76370	0.268442	0.134221	+	0.990951i	$0.457147\pi$
$462$	0	0
$463$	10.6187	0.493494	0.246747	−	0.969080i	$-0.420638\pi$
$463$	10.6187	0.493494	0.246747	+	0.969080i	$0.420638\pi$
$464$	14.9307	0.693140
$465$	−38.4170	−1.78155
$466$	−30.0781	−1.39334
$467$	31.6308	1.46370	0.731849	−	0.681467i	$-0.238658\pi$
$467$	31.6308	1.46370	0.731849	+	0.681467i	$0.238658\pi$
$468$	5.62294	0.259920
$469$	0	0
$470$	25.7131	1.18606
$471$	5.45503	0.251354
$472$	2.77047	0.127521
$473$	0.603560	0.0277517
$474$	−10.7196	−0.492366
$475$	−66.7099	−3.06086
$476$	0	0
$477$	−3.35153	−0.153456
$478$	−25.2493	−1.15487
$479$	39.7627	1.81680	0.908401	−	0.418100i	$-0.137304\pi$
$479$	39.7627	1.81680	0.908401	+	0.418100i	$0.137304\pi$
$480$	29.9180	1.36556
$481$	−21.0971	−0.961943
$482$	−21.8954	−0.997307
$483$	0	0
$484$	−23.7429	−1.07922
$485$	29.1734	1.32469
$486$	2.04183	0.0926194
$487$	−13.8837	−0.629132	−0.314566	−	0.949236i	$-0.601859\pi$
$487$	−13.8837	−0.629132	−0.314566	+	0.949236i	$0.601859\pi$
$488$	−4.53176	−0.205143
$489$	−12.6634	−0.572659
$490$	0	0
$491$	20.2751	0.915001	0.457501	−	0.889209i	$-0.348745\pi$
$491$	20.2751	0.915001	0.457501	+	0.889209i	$0.348745\pi$
$492$	2.16908	0.0977897
$493$	−19.3718	−0.872461
$494$	40.9992	1.84464
$495$	−0.856770	−0.0385089
$496$	37.8314	1.69868
$497$	0	0
$498$	5.12496	0.229655
$499$	9.76966	0.437350	0.218675	−	0.975798i	$-0.429827\pi$
$499$	9.76966	0.437350	0.218675	+	0.975798i	$0.429827\pi$
$500$	−28.9092	−1.29286
$501$	11.4402	0.511110
$502$	21.5451	0.961605
$503$	−6.98768	−0.311565	−0.155783	−	0.987791i	$-0.549790\pi$
$503$	−6.98768	−0.311565	−0.155783	+	0.987791i	$0.549790\pi$
$504$	0	0
$505$	40.0416	1.78183
$506$	−4.02437	−0.178905
$507$	6.27990	0.278900
$508$	33.2720	1.47621
$509$	5.64474	0.250199	0.125099	−	0.992144i	$-0.460075\pi$
$509$	5.64474	0.250199	0.125099	+	0.992144i	$0.460075\pi$
$510$	−35.5118	−1.57249
$511$	0	0
$512$	−31.9705	−1.41291
$513$	7.74581	0.341986
$514$	54.8319	2.41853
$515$	19.5059	0.859532
$516$	−5.63766	−0.248184
$517$	0.792618	0.0348593
$518$	0	0
$519$	12.2561	0.537985
$520$	3.30192	0.144799
$521$	18.6235	0.815910	0.407955	−	0.913002i	$-0.366242\pi$
$521$	18.6235	0.815910	0.407955	+	0.913002i	$0.366242\pi$
$522$	8.39082	0.367256
$523$	−27.5839	−1.20616	−0.603081	−	0.797680i	$-0.706060\pi$
$523$	−27.5839	−1.20616	−0.603081	+	0.797680i	$0.706060\pi$
$524$	37.2481	1.62719
$525$	0	0
$526$	−46.6226	−2.03284
$527$	−49.0842	−2.13814
$528$	0.843709	0.0367177
$529$	49.0380	2.13208
$530$	−25.2482	−1.09671
$531$	−8.02496	−0.348254
$532$	0	0
$533$	−2.59232	−0.112286
$534$	27.1021	1.17282
$535$	−23.0187	−0.995187
$536$	−2.28047	−0.0985014
$537$	6.29779	0.271769
$538$	54.0077	2.32844
$539$	0	0
$540$	8.00281	0.344386
$541$	−16.8601	−0.724873	−0.362437	−	0.932008i	$-0.618055\pi$
$541$	−16.8601	−0.724873	−0.362437	+	0.932008i	$0.618055\pi$
$542$	−17.8722	−0.767675
$543$	−18.8748	−0.809997
$544$	38.2252	1.63889
$545$	−16.3704	−0.701231
$546$	0	0
$547$	−17.8296	−0.762338	−0.381169	−	0.924505i	$-0.624478\pi$
$547$	−17.8296	−0.762338	−0.381169	+	0.924505i	$0.624478\pi$
$548$	19.5765	0.836266
$549$	13.1267	0.560234
$550$	−4.08357	−0.174124
$551$	31.8311	1.35605
$552$	2.93016	0.124716
$553$	0	0
$554$	−13.1646	−0.559311
$555$	−30.0263	−1.27454
$556$	24.0405	1.01954
$557$	−1.21738	−0.0515820	−0.0257910	−	0.999667i	$-0.508210\pi$
$557$	−1.21738	−0.0515820	−0.0257910	+	0.999667i	$0.508210\pi$
$558$	21.2607	0.900036
$559$	6.73770	0.284974
$560$	0	0
$561$	−1.09467	−0.0462169
$562$	44.0824	1.85951
$563$	−12.9116	−0.544157	−0.272079	−	0.962275i	$-0.587711\pi$
$563$	−12.9116	−0.544157	−0.272079	+	0.962275i	$0.587711\pi$
$564$	−7.40359	−0.311747
$565$	−72.2597	−3.03999
$566$	−0.297425	−0.0125017
$567$	0	0
$568$	−1.11588	−0.0468213
$569$	−6.13102	−0.257026	−0.128513	−	0.991708i	$-0.541020\pi$
$569$	−6.13102	−0.257026	−0.128513	+	0.991708i	$0.541020\pi$
$570$	58.3518	2.44409
$571$	−30.1505	−1.26176	−0.630879	−	0.775881i	$-0.717306\pi$
$571$	−30.1505	−1.26176	−0.630879	+	0.775881i	$0.717306\pi$
$572$	1.30575	0.0545962
$573$	−7.98832	−0.333717
$574$	0	0
$575$	73.0977	3.04839
$576$	−9.29063	−0.387109
$577$	−21.8970	−0.911582	−0.455791	−	0.890087i	$-0.650644\pi$
$577$	−21.8970	−0.911582	−0.455791	+	0.890087i	$0.650644\pi$
$578$	−10.6611	−0.443442
$579$	8.36539	0.347654
$580$	32.8872	1.36557
$581$	0	0
$582$	−16.1451	−0.669234
$583$	−0.778287	−0.0322334
$584$	2.28984	0.0947544
$585$	−9.56434	−0.395437
$586$	16.0091	0.661329
$587$	−18.7737	−0.774873	−0.387436	−	0.921896i	$-0.626639\pi$
$587$	−18.7737	−0.774873	−0.387436	+	0.921896i	$0.626639\pi$
$588$	0	0
$589$	80.6536	3.32327
$590$	−60.4547	−2.48888
$591$	20.1945	0.830692
$592$	29.5685	1.21526
$593$	−1.40764	−0.0578048	−0.0289024	−	0.999582i	$-0.509201\pi$
$593$	−1.40764	−0.0578048	−0.0289024	+	0.999582i	$0.509201\pi$
$594$	0.474151	0.0194547
$595$	0	0
$596$	22.1576	0.907610
$597$	−2.42833	−0.0993850
$598$	−44.9251	−1.83712
$599$	−31.7524	−1.29737	−0.648685	−	0.761057i	$-0.724681\pi$
$599$	−31.7524	−1.29737	−0.648685	+	0.761057i	$0.724681\pi$
$600$	2.97327	0.121383
$601$	16.8874	0.688853	0.344427	−	0.938813i	$-0.388073\pi$
$601$	16.8874	0.688853	0.344427	+	0.938813i	$0.388073\pi$
$602$	0	0
$603$	6.60562	0.269002
$604$	−12.4006	−0.504573
$605$	40.3855	1.64190
$606$	−22.1597	−0.900177
$607$	−11.5151	−0.467382	−0.233691	−	0.972311i	$-0.575080\pi$
$607$	−11.5151	−0.467382	−0.233691	+	0.972311i	$0.575080\pi$
$608$	−62.8105	−2.54730
$609$	0	0
$610$	98.8878	4.00385
$611$	8.84820	0.357960
$612$	10.2249	0.413318
$613$	20.5359	0.829438	0.414719	−	0.909949i	$-0.363880\pi$
$613$	20.5359	0.829438	0.414719	+	0.909949i	$0.363880\pi$
$614$	42.6618	1.72169
$615$	−3.68950	−0.148775
$616$	0	0
$617$	1.57898	0.0635675	0.0317837	−	0.999495i	$-0.489881\pi$
$617$	1.57898	0.0635675	0.0317837	+	0.999495i	$0.489881\pi$
$618$	−10.7949	−0.434234
$619$	−34.3577	−1.38095	−0.690476	−	0.723355i	$-0.742599\pi$
$619$	−34.3577	−1.38095	−0.690476	+	0.723355i	$0.742599\pi$
$620$	83.3296	3.34660
$621$	−8.48752	−0.340592
$622$	58.3120	2.33810
$623$	0	0
$624$	9.41854	0.377043
$625$	6.11122	0.244449
$626$	−61.1572	−2.44433
$627$	1.79872	0.0718340
$628$	−11.8324	−0.472164
$629$	−38.3636	−1.52966
$630$	0	0
$631$	−19.9149	−0.792799	−0.396399	−	0.918078i	$-0.629740\pi$
$631$	−19.9149	−0.792799	−0.396399	+	0.918078i	$0.629740\pi$
$632$	1.81246	0.0720958
$633$	10.1756	0.404442
$634$	27.6000	1.09613
$635$	−56.5940	−2.24586
$636$	7.26973	0.288264
$637$	0	0
$638$	1.94850	0.0771420
$639$	3.23226	0.127866
$640$	−10.1534	−0.401350
$641$	24.3992	0.963712	0.481856	−	0.876250i	$-0.339963\pi$
$641$	24.3992	0.963712	0.481856	+	0.876250i	$0.339963\pi$
$642$	12.7390	0.502767
$643$	−42.8135	−1.68840	−0.844200	−	0.536028i	$-0.819924\pi$
$643$	−42.8135	−1.68840	−0.844200	+	0.536028i	$0.819924\pi$
$644$	0	0
$645$	9.58938	0.377582
$646$	74.5542	2.93329
$647$	−9.68055	−0.380582	−0.190291	−	0.981728i	$-0.560943\pi$
$647$	−9.68055	−0.380582	−0.190291	+	0.981728i	$0.560943\pi$
$648$	−0.345232	−0.0135620
$649$	−1.86354	−0.0731505
$650$	−45.5860	−1.78803
$651$	0	0
$652$	27.4679	1.07573
$653$	−35.2294	−1.37863	−0.689317	−	0.724459i	$-0.742089\pi$
$653$	−35.2294	−1.37863	−0.689317	+	0.724459i	$0.742089\pi$
$654$	9.05967	0.354261
$655$	−63.3572	−2.47557
$656$	3.63325	0.141855
$657$	−6.63277	−0.258769
$658$	0	0
$659$	12.3702	0.481875	0.240937	−	0.970541i	$-0.422545\pi$
$659$	12.3702	0.481875	0.240937	+	0.970541i	$0.422545\pi$
$660$	1.85840	0.0723382
$661$	−43.0998	−1.67639	−0.838193	−	0.545373i	$-0.816388\pi$
$661$	−43.0998	−1.67639	−0.838193	+	0.545373i	$0.816388\pi$
$662$	0.973526	0.0378372
$663$	−12.2200	−0.474587
$664$	−0.866525	−0.0336277
$665$	0	0
$666$	16.6171	0.643898
$667$	−34.8791	−1.35052
$668$	−24.8147	−0.960109
$669$	−18.3685	−0.710166
$670$	49.7624	1.92249
$671$	3.04827	0.117677
$672$	0	0
$673$	−41.8091	−1.61162	−0.805811	−	0.592173i	$-0.798270\pi$
$673$	−41.8091	−1.61162	−0.805811	+	0.592173i	$0.798270\pi$
$674$	42.5141	1.63758
$675$	−8.61238	−0.331491
$676$	−13.6216	−0.523908
$677$	−14.7030	−0.565081	−0.282541	−	0.959255i	$-0.591177\pi$
$677$	−14.7030	−0.565081	−0.282541	+	0.959255i	$0.591177\pi$
$678$	39.9898	1.53580
$679$	0	0
$680$	6.00431	0.230255
$681$	−16.6244	−0.637049
$682$	4.93712	0.189052
$683$	25.6649	0.982040	0.491020	−	0.871148i	$-0.336624\pi$
$683$	25.6649	0.982040	0.491020	+	0.871148i	$0.336624\pi$
$684$	−16.8013	−0.642413
$685$	−33.2986	−1.27228
$686$	0	0
$687$	15.2296	0.581045
$688$	−9.44320	−0.360019
$689$	−8.68822	−0.330995
$690$	−63.9393	−2.43413
$691$	20.9970	0.798763	0.399381	−	0.916785i	$-0.369225\pi$
$691$	20.9970	0.798763	0.399381	+	0.916785i	$0.369225\pi$
$692$	−26.5846	−1.01059
$693$	0	0
$694$	−18.6168	−0.706684
$695$	−40.8917	−1.55111
$696$	−1.41872	−0.0537763
$697$	−4.71395	−0.178554
$698$	21.4018	0.810070
$699$	−14.7310	−0.557176
$700$	0	0
$701$	12.6745	0.478709	0.239355	−	0.970932i	$-0.423064\pi$
$701$	12.6745	0.478709	0.239355	+	0.970932i	$0.423064\pi$
$702$	5.29308	0.199774
$703$	63.0378	2.37751
$704$	−2.15746	−0.0813122
$705$	12.5931	0.474285
$706$	−8.84974	−0.333064
$707$	0	0
$708$	17.4068	0.654187
$709$	2.37978	0.0893745	0.0446873	−	0.999001i	$-0.485771\pi$
$709$	2.37978	0.0893745	0.0446873	+	0.999001i	$0.485771\pi$
$710$	24.3497	0.913829
$711$	−5.24998	−0.196890
$712$	−4.58241	−0.171733
$713$	−88.3766	−3.30973
$714$	0	0
$715$	−2.22102	−0.0830613
$716$	−13.6604	−0.510513
$717$	−12.3660	−0.461816
$718$	−3.34094	−0.124683
$719$	−13.3645	−0.498410	−0.249205	−	0.968451i	$-0.580169\pi$
$719$	−13.3645	−0.498410	−0.249205	+	0.968451i	$0.580169\pi$
$720$	13.4049	0.499570
$721$	0	0
$722$	−83.7102	−3.11537
$723$	−10.7234	−0.398807
$724$	40.9410	1.52156
$725$	−35.3922	−1.31443
$726$	−22.3500	−0.829488
$727$	3.33356	0.123635	0.0618175	−	0.998087i	$-0.480310\pi$
$727$	3.33356	0.123635	0.0618175	+	0.998087i	$0.480310\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−49.9668	−1.84936
$731$	12.2520	0.453158
$732$	−28.4729	−1.05239
$733$	−40.5226	−1.49674	−0.748368	−	0.663284i	$-0.769162\pi$
$733$	−40.5226	−1.49674	−0.748368	+	0.663284i	$0.769162\pi$
$734$	−40.2003	−1.48382
$735$	0	0
$736$	68.8249	2.53692
$737$	1.53395	0.0565037
$738$	2.04183	0.0751609
$739$	0.959701	0.0353032	0.0176516	−	0.999844i	$-0.494381\pi$
$739$	0.959701	0.0353032	0.0176516	+	0.999844i	$0.494381\pi$
$740$	65.1293	2.39420
$741$	20.0796	0.737642
$742$	0	0
$743$	−12.4405	−0.456399	−0.228200	−	0.973614i	$-0.573284\pi$
$743$	−12.4405	−0.456399	−0.228200	+	0.973614i	$0.573284\pi$
$744$	−3.59474	−0.131790
$745$	−37.6889	−1.38082
$746$	3.96059	0.145007
$747$	2.50998	0.0918354
$748$	2.37442	0.0868174
$749$	0	0
$750$	−27.2133	−0.993689
$751$	−46.6636	−1.70278	−0.851390	−	0.524534i	$-0.824240\pi$
$751$	−46.6636	−1.70278	−0.851390	+	0.524534i	$0.824240\pi$
$752$	−12.4012	−0.452224
$753$	10.5518	0.384531
$754$	21.7517	0.792149
$755$	21.0928	0.767646
$756$	0	0
$757$	−14.4610	−0.525593	−0.262796	−	0.964851i	$-0.584645\pi$
$757$	−14.4610	−0.525593	−0.262796	+	0.964851i	$0.584645\pi$
$758$	7.09588	0.257734
$759$	−1.97096	−0.0715413
$760$	−9.86609	−0.357881
$761$	−12.7440	−0.461971	−0.230985	−	0.972957i	$-0.574195\pi$
$761$	−12.7440	−0.461971	−0.230985	+	0.972957i	$0.574195\pi$
$762$	31.3201	1.13461
$763$	0	0
$764$	17.3273	0.626880
$765$	−17.3921	−0.628813
$766$	20.4345	0.738330
$767$	−20.8032	−0.751161
$768$	−12.9622	−0.467732
$769$	13.1820	0.475354	0.237677	−	0.971344i	$-0.423614\pi$
$769$	13.1820	0.475354	0.237677	+	0.971344i	$0.423614\pi$
$770$	0	0
$771$	26.8542	0.967132
$772$	−18.1452	−0.653060
$773$	7.05456	0.253735	0.126867	−	0.991920i	$-0.459508\pi$
$773$	7.05456	0.253735	0.126867	+	0.991920i	$0.459508\pi$
$774$	−5.30693	−0.190754
$775$	−89.6768	−3.22128
$776$	2.72980	0.0979940
$777$	0	0
$778$	−44.4235	−1.59266
$779$	7.74581	0.277522
$780$	20.7458	0.742819
$781$	0.750592	0.0268583
$782$	−81.6932	−2.92134
$783$	4.10946	0.146860
$784$	0	0
$785$	20.1263	0.718338
$786$	35.0630	1.25065
$787$	−27.9275	−0.995507	−0.497754	−	0.867318i	$-0.665842\pi$
$787$	−27.9275	−0.995507	−0.497754	+	0.867318i	$0.665842\pi$
$788$	−43.8036	−1.56044
$789$	−22.8337	−0.812901
$790$	−39.5498	−1.40712
$791$	0	0
$792$	−0.0801693	−0.00284869
$793$	34.0286	1.20839
$794$	−48.2349	−1.71179
$795$	−12.3655	−0.438558
$796$	5.26725	0.186693
$797$	−35.5823	−1.26039	−0.630196	−	0.776436i	$-0.717025\pi$
$797$	−35.5823	−1.26039	−0.630196	+	0.776436i	$0.717025\pi$
$798$	0	0
$799$	16.0898	0.569218
$800$	69.8374	2.46913
$801$	13.2734	0.468993
$802$	7.49726	0.264738
$803$	−1.54025	−0.0543543
$804$	−14.3281	−0.505314
$805$	0	0
$806$	55.1144	1.94132
$807$	26.4506	0.931105
$808$	3.74675	0.131810
$809$	−35.9909	−1.26537	−0.632686	−	0.774408i	$-0.718048\pi$
$809$	−35.9909	−1.26537	−0.632686	+	0.774408i	$0.718048\pi$
$810$	7.53333	0.264694
$811$	−26.9511	−0.946380	−0.473190	−	0.880960i	$-0.656898\pi$
$811$	−26.9511	−0.946380	−0.473190	+	0.880960i	$0.656898\pi$
$812$	0	0
$813$	−8.75300	−0.306981
$814$	3.85879	0.135251
$815$	−46.7216	−1.63659
$816$	17.1270	0.599564
$817$	−20.1322	−0.704335
$818$	−38.0199	−1.32934
$819$	0	0
$820$	8.00281	0.279470
$821$	15.8769	0.554109	0.277054	−	0.960854i	$-0.410642\pi$
$821$	15.8769	0.554109	0.277054	+	0.960854i	$0.410642\pi$
$822$	18.4280	0.642752
$823$	27.5922	0.961803	0.480902	−	0.876775i	$-0.340309\pi$
$823$	27.5922	0.961803	0.480902	+	0.876775i	$0.340309\pi$
$824$	1.82520	0.0635837
$825$	−1.99996	−0.0696295
$826$	0	0
$827$	−25.0669	−0.871661	−0.435831	−	0.900029i	$-0.643545\pi$
$827$	−25.0669	−0.871661	−0.435831	+	0.900029i	$0.643545\pi$
$828$	18.4101	0.639795
$829$	−41.4853	−1.44084	−0.720422	−	0.693536i	$-0.756052\pi$
$829$	−41.4853	−1.44084	−0.720422	+	0.693536i	$0.756052\pi$
$830$	18.9085	0.656324
$831$	−6.44745	−0.223659
$832$	−24.0842	−0.834971
$833$	0	0
$834$	22.6302	0.783619
$835$	42.2085	1.46069
$836$	−3.90157	−0.134939
$837$	10.4125	0.359910
$838$	41.6269	1.43798
$839$	−3.49825	−0.120773	−0.0603865	−	0.998175i	$-0.519233\pi$
$839$	−3.49825	−0.120773	−0.0603865	+	0.998175i	$0.519233\pi$
$840$	0	0
$841$	−12.1124	−0.417668
$842$	49.9075	1.71993
$843$	21.5896	0.743587
$844$	−22.0716	−0.759735
$845$	23.1697	0.797060
$846$	−6.96926	−0.239608
$847$	0	0
$848$	12.1770	0.418158
$849$	−0.145666	−0.00499924
$850$	−82.8950	−2.84328
$851$	−69.0740	−2.36783
$852$	−7.01104	−0.240194
$853$	46.0844	1.57790	0.788950	−	0.614458i	$-0.210625\pi$
$853$	46.0844	1.57790	0.788950	+	0.614458i	$0.210625\pi$
$854$	0	0
$855$	28.5781	0.977352
$856$	−2.15390	−0.0736188
$857$	−48.0142	−1.64013	−0.820067	−	0.572267i	$-0.806064\pi$
$857$	−48.0142	−1.64013	−0.820067	+	0.572267i	$0.806064\pi$
$858$	1.22915	0.0419625
$859$	−20.2044	−0.689365	−0.344682	−	0.938719i	$-0.612013\pi$
$859$	−20.2044	−0.689365	−0.344682	+	0.938719i	$0.612013\pi$
$860$	−20.8001	−0.709279
$861$	0	0
$862$	−16.0022	−0.545037
$863$	−15.4157	−0.524755	−0.262377	−	0.964965i	$-0.584507\pi$
$863$	−15.4157	−0.524755	−0.262377	+	0.964965i	$0.584507\pi$
$864$	−8.10896	−0.275872
$865$	45.2190	1.53749
$866$	−21.7501	−0.739097
$867$	−5.22132	−0.177325
$868$	0	0
$869$	−1.21914	−0.0413566
$870$	30.9579	1.04957
$871$	17.1239	0.580220
$872$	−1.53180	−0.0518734
$873$	−7.90714	−0.267616
$874$	134.236	4.54059
$875$	0	0
$876$	14.3870	0.486092
$877$	14.7504	0.498084	0.249042	−	0.968493i	$-0.419884\pi$
$877$	14.7504	0.498084	0.249042	+	0.968493i	$0.419884\pi$
$878$	50.3314	1.69860
$879$	7.84054	0.264455
$880$	3.11286	0.104935
$881$	33.7312	1.13643	0.568216	−	0.822879i	$-0.307634\pi$
$881$	33.7312	1.13643	0.568216	+	0.822879i	$0.307634\pi$
$882$	0	0
$883$	16.2628	0.547286	0.273643	−	0.961831i	$-0.411771\pi$
$883$	16.2628	0.547286	0.273643	+	0.961831i	$0.411771\pi$
$884$	26.5063	0.891502
$885$	−29.6081	−0.995264
$886$	1.81362	0.0609299
$887$	32.9783	1.10730	0.553651	−	0.832749i	$-0.313234\pi$
$887$	32.9783	1.10730	0.553651	+	0.832749i	$0.313234\pi$
$888$	−2.80960	−0.0942841
$889$	0	0
$890$	99.9931	3.35178
$891$	0.232219	0.00777962
$892$	39.8427	1.33403
$893$	−26.4383	−0.884724
$894$	20.8577	0.697587
$895$	23.2357	0.776682
$896$	0	0
$897$	−22.0023	−0.734636
$898$	40.1724	1.34057
$899$	42.7899	1.42712
$900$	18.6809	0.622698
$901$	−15.7989	−0.526339
$902$	0.474151	0.0157875
$903$	0	0
$904$	−6.76145	−0.224883
$905$	−69.6386	−2.31487
$906$	−11.6731	−0.387814
$907$	−14.9899	−0.497732	−0.248866	−	0.968538i	$-0.580058\pi$
$907$	−14.9899	−0.497732	−0.248866	+	0.968538i	$0.580058\pi$
$908$	36.0597	1.19668
$909$	−10.8529	−0.359967
$910$	0	0
$911$	37.8616	1.25441	0.627205	−	0.778854i	$-0.284199\pi$
$911$	37.8616	1.25441	0.627205	+	0.778854i	$0.284199\pi$
$912$	−28.1425	−0.931891
$913$	0.582864	0.0192900
$914$	17.8971	0.591982
$915$	48.4309	1.60108
$916$	−33.0342	−1.09148
$917$	0	0
$918$	9.62509	0.317675
$919$	−27.0097	−0.890967	−0.445484	−	0.895290i	$-0.646968\pi$
$919$	−27.0097	−0.890967	−0.445484	+	0.895290i	$0.646968\pi$
$920$	10.8108	0.356422
$921$	20.8939	0.688476
$922$	−11.7685	−0.387575
$923$	8.37905	0.275800
$924$	0	0
$925$	−70.0902	−2.30455
$926$	−21.6817	−0.712503
$927$	−5.28687	−0.173644
$928$	−33.3234	−1.09389
$929$	−2.99013	−0.0981030	−0.0490515	−	0.998796i	$-0.515620\pi$
$929$	−2.99013	−0.0981030	−0.0490515	+	0.998796i	$0.515620\pi$
$930$	78.4411	2.57219
$931$	0	0
$932$	31.9526	1.04664
$933$	28.5586	0.934968
$934$	−64.5848	−2.11328
$935$	−4.03877	−0.132082
$936$	−0.894950	−0.0292524
$937$	24.0009	0.784076	0.392038	−	0.919949i	$-0.371770\pi$
$937$	24.0009	0.784076	0.392038	+	0.919949i	$0.371770\pi$
$938$	0	0
$939$	−29.9521	−0.977450
$940$	−27.3155	−0.890934
$941$	−3.18393	−0.103793	−0.0518966	−	0.998652i	$-0.516527\pi$
$941$	−3.18393	−0.103793	−0.0518966	+	0.998652i	$0.516527\pi$
$942$	−11.1382	−0.362904
$943$	−8.48752	−0.276392
$944$	29.1567	0.948970
$945$	0	0
$946$	−1.23237	−0.0400678
$947$	15.3342	0.498295	0.249147	−	0.968466i	$-0.419850\pi$
$947$	15.3342	0.498295	0.249147	+	0.968466i	$0.419850\pi$
$948$	11.3876	0.369853
$949$	−17.1942	−0.558148
$950$	136.210	4.41925
$951$	13.5173	0.438327
$952$	0	0
$953$	25.9900	0.841900	0.420950	−	0.907084i	$-0.361697\pi$
$953$	25.9900	0.841900	0.420950	+	0.907084i	$0.361697\pi$
$954$	6.84326	0.221559
$955$	−29.4729	−0.953720
$956$	26.8228	0.867511
$957$	0.954292	0.0308479
$958$	−81.1887	−2.62309
$959$	0	0
$960$	−34.2777	−1.10631
$961$	77.4210	2.49745
$962$	43.0767	1.38885
$963$	6.23899	0.201049
$964$	23.2599	0.749151
$965$	30.8641	0.993549
$966$	0	0
$967$	5.70119	0.183338	0.0916689	−	0.995790i	$-0.470780\pi$
$967$	5.70119	0.183338	0.0916689	+	0.995790i	$0.470780\pi$
$968$	3.77893	0.121460
$969$	36.5134	1.17298
$970$	−59.5671	−1.91258
$971$	46.4697	1.49128	0.745642	−	0.666347i	$-0.232143\pi$
$971$	46.4697	1.49128	0.745642	+	0.666347i	$0.232143\pi$
$972$	−2.16908	−0.0695733
$973$	0	0
$974$	28.3482	0.908336
$975$	−22.3260	−0.715005
$976$	−47.6926	−1.52660
$977$	12.1107	0.387455	0.193728	−	0.981055i	$-0.437942\pi$
$977$	12.1107	0.387455	0.193728	+	0.981055i	$0.437942\pi$
$978$	25.8565	0.826801
$979$	3.08233	0.0985118
$980$	0	0
$981$	4.43703	0.141663
$982$	−41.3983	−1.32107
$983$	37.1662	1.18542	0.592709	−	0.805417i	$-0.298058\pi$
$983$	37.1662	1.18542	0.592709	+	0.805417i	$0.298058\pi$
$984$	−0.345232	−0.0110056
$985$	74.5077	2.37401
$986$	39.5539	1.25965
$987$	0	0
$988$	−43.5542	−1.38564
$989$	22.0599	0.701465
$990$	1.74938	0.0555989
$991$	−25.6087	−0.813486	−0.406743	−	0.913543i	$-0.633336\pi$
$991$	−25.6087	−0.813486	−0.406743	+	0.913543i	$0.633336\pi$
$992$	−84.4348	−2.68081
$993$	0.476790	0.0151305
$994$	0	0
$995$	−8.95932	−0.284030
$996$	−5.44435	−0.172511
$997$	4.04117	0.127985	0.0639925	−	0.997950i	$-0.479617\pi$
$997$	4.04117	0.127985	0.0639925	+	0.997950i	$0.479617\pi$
$998$	−19.9480	−0.631443
$999$	8.13831	0.257485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bb.1.2		8
7.2	even	3		861.2.i.d.739.7	yes	16
7.4	even	3		861.2.i.d.247.7	✓	16
7.6	odd	2		6027.2.a.bc.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.d.247.7	✓	16	7.4	even	3
861.2.i.d.739.7	yes	16	7.2	even	3
6027.2.a.bb.1.2		8	1.1	even	1	trivial
6027.2.a.bc.1.2		8	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.04183 q^{2} -1.00000 q^{3} +2.16908 q^{4} -3.68950 q^{5} +2.04183 q^{6} -0.345232 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.04183 q^{2} -1.00000 q^{3} +2.16908 q^{4} -3.68950 q^{5} +2.04183 q^{6} -0.345232 q^{8} +1.00000 q^{9} +7.53333 q^{10} +0.232219 q^{11} -2.16908 q^{12} +2.59232 q^{13} +3.68950 q^{15} -3.63325 q^{16} +4.71395 q^{17} -2.04183 q^{18} -7.74581 q^{19} -8.00281 q^{20} -0.474151 q^{22} +8.48752 q^{23} +0.345232 q^{24} +8.61238 q^{25} -5.29308 q^{26} -1.00000 q^{27} -4.10946 q^{29} -7.53333 q^{30} -10.4125 q^{31} +8.10896 q^{32} -0.232219 q^{33} -9.62509 q^{34} +2.16908 q^{36} -8.13831 q^{37} +15.8156 q^{38} -2.59232 q^{39} +1.27373 q^{40} -1.00000 q^{41} +2.59910 q^{43} +0.503701 q^{44} -3.68950 q^{45} -17.3301 q^{46} +3.41324 q^{47} +3.63325 q^{48} -17.5850 q^{50} -4.71395 q^{51} +5.62294 q^{52} -3.35153 q^{53} +2.04183 q^{54} -0.856770 q^{55} +7.74581 q^{57} +8.39082 q^{58} -8.02496 q^{59} +8.00281 q^{60} +13.1267 q^{61} +21.2607 q^{62} -9.29063 q^{64} -9.56434 q^{65} +0.474151 q^{66} +6.60562 q^{67} +10.2249 q^{68} -8.48752 q^{69} +3.23226 q^{71} -0.345232 q^{72} -6.63277 q^{73} +16.6171 q^{74} -8.61238 q^{75} -16.8013 q^{76} +5.29308 q^{78} -5.24998 q^{79} +13.4049 q^{80} +1.00000 q^{81} +2.04183 q^{82} +2.50998 q^{83} -17.3921 q^{85} -5.30693 q^{86} +4.10946 q^{87} -0.0801693 q^{88} +13.2734 q^{89} +7.53333 q^{90} +18.4101 q^{92} +10.4125 q^{93} -6.96926 q^{94} +28.5781 q^{95} -8.10896 q^{96} -7.90714 q^{97} +0.232219 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 8 q^{3} + 13 q^{4} - 7 q^{5} - q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + q^2 - 8 * q^3 + 13 * q^4 - 7 * q^5 - q^6 + 6 * q^8 + 8 * q^9	\( 8 q + q^{2} - 8 q^{3} + 13 q^{4} - 7 q^{5} - q^{6} + 6 q^{8} + 8 q^{9} - 8 q^{10} + 11 q^{11} - 13 q^{12} - 10 q^{13} + 7 q^{15} - 17 q^{16} - 3 q^{17} + q^{18} - 6 q^{19} - 11 q^{20} + 15 q^{22} + 14 q^{23} - 6 q^{24} + 25 q^{25} - 24 q^{26} - 8 q^{27} + 2 q^{29} + 8 q^{30} - 16 q^{31} + 3 q^{32} - 11 q^{33} + 4 q^{34} + 13 q^{36} - 20 q^{37} - 10 q^{38} + 10 q^{39} + 3 q^{40} - 8 q^{41} + 7 q^{43} - 7 q^{45} - 5 q^{46} - 14 q^{47} + 17 q^{48} - 5 q^{50} + 3 q^{51} - 23 q^{52} + 7 q^{53} - q^{54} - 48 q^{55} + 6 q^{57} - 20 q^{58} - 22 q^{59} + 11 q^{60} + 33 q^{62} - 10 q^{64} - 14 q^{65} - 15 q^{66} + 12 q^{67} + 27 q^{68} - 14 q^{69} - 5 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} - 25 q^{75} - 43 q^{76} + 24 q^{78} - 15 q^{79} + 7 q^{80} + 8 q^{81} - q^{82} - 15 q^{83} - 43 q^{85} + 31 q^{86} - 2 q^{87} + 17 q^{88} - 29 q^{89} - 8 q^{90} + 19 q^{92} + 16 q^{93} - 20 q^{94} + 14 q^{95} - 3 q^{96} - 19 q^{97} + 11 q^{99}+O(q^{100}) \) 8 * q + q^2 - 8 * q^3 + 13 * q^4 - 7 * q^5 - q^6 + 6 * q^8 + 8 * q^9 - 8 * q^10 + 11 * q^11 - 13 * q^12 - 10 * q^13 + 7 * q^15 - 17 * q^16 - 3 * q^17 + q^18 - 6 * q^19 - 11 * q^20 + 15 * q^22 + 14 * q^23 - 6 * q^24 + 25 * q^25 - 24 * q^26 - 8 * q^27 + 2 * q^29 + 8 * q^30 - 16 * q^31 + 3 * q^32 - 11 * q^33 + 4 * q^34 + 13 * q^36 - 20 * q^37 - 10 * q^38 + 10 * q^39 + 3 * q^40 - 8 * q^41 + 7 * q^43 - 7 * q^45 - 5 * q^46 - 14 * q^47 + 17 * q^48 - 5 * q^50 + 3 * q^51 - 23 * q^52 + 7 * q^53 - q^54 - 48 * q^55 + 6 * q^57 - 20 * q^58 - 22 * q^59 + 11 * q^60 + 33 * q^62 - 10 * q^64 - 14 * q^65 - 15 * q^66 + 12 * q^67 + 27 * q^68 - 14 * q^69 - 5 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 - 25 * q^75 - 43 * q^76 + 24 * q^78 - 15 * q^79 + 7 * q^80 + 8 * q^81 - q^82 - 15 * q^83 - 43 * q^85 + 31 * q^86 - 2 * q^87 + 17 * q^88 - 29 * q^89 - 8 * q^90 + 19 * q^92 + 16 * q^93 - 20 * q^94 + 14 * q^95 - 3 * q^96 - 19 * q^97 + 11 * q^99

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